Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space

Abstract In 2013, a minimax method for finding saddle points of locally Lipschitz continuous functional was designed (Yao Math. Comp. 82 2087–2136 2013). The method can be applied to numerically solve hemivariational inequality for multiple solutions. Its subsequence and sequence convergence results...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Yao, Xudong [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2016

Schlagwörter:	Minimax method Hemivariational inequality Finite element method Convergence

Übergeordnetes Werk:	Enthalten in: Advances in computational mathematics - Bussum : Baltzer Science Publ., 1993, 42(2016), 6 vom: 14. Juli, Seite 1331-1362
Übergeordnetes Werk:	volume:42 ; year:2016 ; number:6 ; day:14 ; month:07 ; pages:1331-1362

Links:	Volltext

DOI / URN:	10.1007/s10444-016-9465-0

Katalog-ID:	SPR010110143

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520			\|a Abstract In 2013, a minimax method for finding saddle points of locally Lipschitz continuous functional was designed (Yao Math. Comp. 82 2087–2136 2013). The method can be applied to numerically solve hemivariational inequality for multiple solutions. Its subsequence and sequence convergence results in functional analysis were established in the same paper. But, since these convergence results do not consider discretization, they are not convergence results in numerical analysis. In this paper, we point out what approximation problem is, when this minimax method is used to solve hemivariational inequality and the finite element method is used in discretization. Computation of the approximation problem is discussed, numerical experiment is carried out and its global convergence is verified. Finally, as element size goes to zero, convergence of solutions of the approximation problem to solutions of hemivariational inequality is proved.
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912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
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912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
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912			\|a GBV_ILN_4333
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matchkey_str	article:15729044:2016----::ovrecaayioaiiamtofridnmlilsltosfeiait
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allfields	10.1007/s10444-016-9465-0 doi (DE-627)SPR010110143 (SPR)s10444-016-9465-0-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Yao, Xudong verfasserin aut Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In 2013, a minimax method for finding saddle points of locally Lipschitz continuous functional was designed (Yao Math. Comp. 82 2087–2136 2013). The method can be applied to numerically solve hemivariational inequality for multiple solutions. Its subsequence and sequence convergence results in functional analysis were established in the same paper. But, since these convergence results do not consider discretization, they are not convergence results in numerical analysis. In this paper, we point out what approximation problem is, when this minimax method is used to solve hemivariational inequality and the finite element method is used in discretization. Computation of the approximation problem is discussed, numerical experiment is carried out and its global convergence is verified. Finally, as element size goes to zero, convergence of solutions of the approximation problem to solutions of hemivariational inequality is proved. Minimax method (dpeaa)DE-He213 Hemivariational inequality (dpeaa)DE-He213 Finite element method (dpeaa)DE-He213 Convergence (dpeaa)DE-He213 Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 42(2016), 6 vom: 14. Juli, Seite 1331-1362 (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:42 year:2016 number:6 day:14 month:07 pages:1331-1362 https://dx.doi.org/10.1007/s10444-016-9465-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 42 2016 6 14 07 1331-1362
spelling	10.1007/s10444-016-9465-0 doi (DE-627)SPR010110143 (SPR)s10444-016-9465-0-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Yao, Xudong verfasserin aut Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In 2013, a minimax method for finding saddle points of locally Lipschitz continuous functional was designed (Yao Math. Comp. 82 2087–2136 2013). The method can be applied to numerically solve hemivariational inequality for multiple solutions. Its subsequence and sequence convergence results in functional analysis were established in the same paper. But, since these convergence results do not consider discretization, they are not convergence results in numerical analysis. In this paper, we point out what approximation problem is, when this minimax method is used to solve hemivariational inequality and the finite element method is used in discretization. Computation of the approximation problem is discussed, numerical experiment is carried out and its global convergence is verified. Finally, as element size goes to zero, convergence of solutions of the approximation problem to solutions of hemivariational inequality is proved. Minimax method (dpeaa)DE-He213 Hemivariational inequality (dpeaa)DE-He213 Finite element method (dpeaa)DE-He213 Convergence (dpeaa)DE-He213 Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 42(2016), 6 vom: 14. Juli, Seite 1331-1362 (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:42 year:2016 number:6 day:14 month:07 pages:1331-1362 https://dx.doi.org/10.1007/s10444-016-9465-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 42 2016 6 14 07 1331-1362
allfields_unstemmed	10.1007/s10444-016-9465-0 doi (DE-627)SPR010110143 (SPR)s10444-016-9465-0-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Yao, Xudong verfasserin aut Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In 2013, a minimax method for finding saddle points of locally Lipschitz continuous functional was designed (Yao Math. Comp. 82 2087–2136 2013). The method can be applied to numerically solve hemivariational inequality for multiple solutions. Its subsequence and sequence convergence results in functional analysis were established in the same paper. But, since these convergence results do not consider discretization, they are not convergence results in numerical analysis. In this paper, we point out what approximation problem is, when this minimax method is used to solve hemivariational inequality and the finite element method is used in discretization. Computation of the approximation problem is discussed, numerical experiment is carried out and its global convergence is verified. Finally, as element size goes to zero, convergence of solutions of the approximation problem to solutions of hemivariational inequality is proved. Minimax method (dpeaa)DE-He213 Hemivariational inequality (dpeaa)DE-He213 Finite element method (dpeaa)DE-He213 Convergence (dpeaa)DE-He213 Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 42(2016), 6 vom: 14. Juli, Seite 1331-1362 (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:42 year:2016 number:6 day:14 month:07 pages:1331-1362 https://dx.doi.org/10.1007/s10444-016-9465-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 42 2016 6 14 07 1331-1362
allfieldsGer	10.1007/s10444-016-9465-0 doi (DE-627)SPR010110143 (SPR)s10444-016-9465-0-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Yao, Xudong verfasserin aut Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In 2013, a minimax method for finding saddle points of locally Lipschitz continuous functional was designed (Yao Math. Comp. 82 2087–2136 2013). The method can be applied to numerically solve hemivariational inequality for multiple solutions. Its subsequence and sequence convergence results in functional analysis were established in the same paper. But, since these convergence results do not consider discretization, they are not convergence results in numerical analysis. In this paper, we point out what approximation problem is, when this minimax method is used to solve hemivariational inequality and the finite element method is used in discretization. Computation of the approximation problem is discussed, numerical experiment is carried out and its global convergence is verified. Finally, as element size goes to zero, convergence of solutions of the approximation problem to solutions of hemivariational inequality is proved. Minimax method (dpeaa)DE-He213 Hemivariational inequality (dpeaa)DE-He213 Finite element method (dpeaa)DE-He213 Convergence (dpeaa)DE-He213 Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 42(2016), 6 vom: 14. Juli, Seite 1331-1362 (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:42 year:2016 number:6 day:14 month:07 pages:1331-1362 https://dx.doi.org/10.1007/s10444-016-9465-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 42 2016 6 14 07 1331-1362
allfieldsSound	10.1007/s10444-016-9465-0 doi (DE-627)SPR010110143 (SPR)s10444-016-9465-0-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Yao, Xudong verfasserin aut Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In 2013, a minimax method for finding saddle points of locally Lipschitz continuous functional was designed (Yao Math. Comp. 82 2087–2136 2013). The method can be applied to numerically solve hemivariational inequality for multiple solutions. Its subsequence and sequence convergence results in functional analysis were established in the same paper. But, since these convergence results do not consider discretization, they are not convergence results in numerical analysis. In this paper, we point out what approximation problem is, when this minimax method is used to solve hemivariational inequality and the finite element method is used in discretization. Computation of the approximation problem is discussed, numerical experiment is carried out and its global convergence is verified. Finally, as element size goes to zero, convergence of solutions of the approximation problem to solutions of hemivariational inequality is proved. Minimax method (dpeaa)DE-He213 Hemivariational inequality (dpeaa)DE-He213 Finite element method (dpeaa)DE-He213 Convergence (dpeaa)DE-He213 Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 42(2016), 6 vom: 14. Juli, Seite 1331-1362 (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:42 year:2016 number:6 day:14 month:07 pages:1331-1362 https://dx.doi.org/10.1007/s10444-016-9465-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 42 2016 6 14 07 1331-1362
language	English
source	Enthalten in Advances in computational mathematics 42(2016), 6 vom: 14. Juli, Seite 1331-1362 volume:42 year:2016 number:6 day:14 month:07 pages:1331-1362
sourceStr	Enthalten in Advances in computational mathematics 42(2016), 6 vom: 14. Juli, Seite 1331-1362 volume:42 year:2016 number:6 day:14 month:07 pages:1331-1362
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Minimax method Hemivariational inequality Finite element method Convergence
dewey-raw	510
isfreeaccess_bool	false
container_title	Advances in computational mathematics
authorswithroles_txt_mv	Yao, Xudong @@aut@@
publishDateDaySort_date	2016-07-14T00:00:00Z
hierarchy_top_id	320506533
dewey-sort	3510
id	SPR010110143
language_de	englisch
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author	Yao, Xudong
spellingShingle	Yao, Xudong ddc 510 bkl 31.76 misc Minimax method misc Hemivariational inequality misc Finite element method misc Convergence Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space
authorStr	Yao, Xudong
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topic_title	510 ASE 31.76 bkl Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space Minimax method (dpeaa)DE-He213 Hemivariational inequality (dpeaa)DE-He213 Finite element method (dpeaa)DE-He213 Convergence (dpeaa)DE-He213
topic	ddc 510 bkl 31.76 misc Minimax method misc Hemivariational inequality misc Finite element method misc Convergence
topic_unstemmed	ddc 510 bkl 31.76 misc Minimax method misc Hemivariational inequality misc Finite element method misc Convergence
topic_browse	ddc 510 bkl 31.76 misc Minimax method misc Hemivariational inequality misc Finite element method misc Convergence
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title	Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space
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title_full	Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space
author_sort	Yao, Xudong
journal	Advances in computational mathematics
journalStr	Advances in computational mathematics
lang_code	eng
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author_browse	Yao, Xudong
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doi_str_mv	10.1007/s10444-016-9465-0
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title_sort	convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in hilbert space
title_auth	Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space
abstract	Abstract In 2013, a minimax method for finding saddle points of locally Lipschitz continuous functional was designed (Yao Math. Comp. 82 2087–2136 2013). The method can be applied to numerically solve hemivariational inequality for multiple solutions. Its subsequence and sequence convergence results in functional analysis were established in the same paper. But, since these convergence results do not consider discretization, they are not convergence results in numerical analysis. In this paper, we point out what approximation problem is, when this minimax method is used to solve hemivariational inequality and the finite element method is used in discretization. Computation of the approximation problem is discussed, numerical experiment is carried out and its global convergence is verified. Finally, as element size goes to zero, convergence of solutions of the approximation problem to solutions of hemivariational inequality is proved.
abstractGer	Abstract In 2013, a minimax method for finding saddle points of locally Lipschitz continuous functional was designed (Yao Math. Comp. 82 2087–2136 2013). The method can be applied to numerically solve hemivariational inequality for multiple solutions. Its subsequence and sequence convergence results in functional analysis were established in the same paper. But, since these convergence results do not consider discretization, they are not convergence results in numerical analysis. In this paper, we point out what approximation problem is, when this minimax method is used to solve hemivariational inequality and the finite element method is used in discretization. Computation of the approximation problem is discussed, numerical experiment is carried out and its global convergence is verified. Finally, as element size goes to zero, convergence of solutions of the approximation problem to solutions of hemivariational inequality is proved.
abstract_unstemmed	Abstract In 2013, a minimax method for finding saddle points of locally Lipschitz continuous functional was designed (Yao Math. Comp. 82 2087–2136 2013). The method can be applied to numerically solve hemivariational inequality for multiple solutions. Its subsequence and sequence convergence results in functional analysis were established in the same paper. But, since these convergence results do not consider discretization, they are not convergence results in numerical analysis. In this paper, we point out what approximation problem is, when this minimax method is used to solve hemivariational inequality and the finite element method is used in discretization. Computation of the approximation problem is discussed, numerical experiment is carried out and its global convergence is verified. Finally, as element size goes to zero, convergence of solutions of the approximation problem to solutions of hemivariational inequality is proved.
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title_short	Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space
url	https://dx.doi.org/10.1007/s10444-016-9465-0
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doi_str	10.1007/s10444-016-9465-0
up_date	2024-07-03T14:00:02.945Z
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Comp. 82 2087–2136 2013). The method can be applied to numerically solve hemivariational inequality for multiple solutions. Its subsequence and sequence convergence results in functional analysis were established in the same paper. But, since these convergence results do not consider discretization, they are not convergence results in numerical analysis. In this paper, we point out what approximation problem is, when this minimax method is used to solve hemivariational inequality and the finite element method is used in discretization. Computation of the approximation problem is discussed, numerical experiment is carried out and its global convergence is verified. 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